[Feature] C4v CTMRG

[Yue-Zhengyuan]

I noticed recently an article which improves the speed of C4v CTMRG using QR-decompositions:

https://arxiv.org/abs/2505.00494

The accompanying code repo is https://github.com/qiyang-ustc/QRCTM. At the end of the article they commented that it might be possible to adapt this method to arbitrary unit cells without C4v symmetry. I think it will be of interest to @pbrehmer and TNRKit people (@VictorVanthilt @dartsushi) who are not satisfied with the current performance of PEPSKit.

[ogauthe]

I already wrote a C4v CTMRG algorithm. I plan to merge it in PEPSKit at some point but I would like to use TensorKit.jl version of truncated_eigh, which is not implemented yet.

You may have a look at https://github.com/ogauthe/C4vCTMRG.jl

I did not know that new version of it, I will have a look thanks!

[VictorVanthilt]

Say it louder for the people in the back 📢! We need our truncated eigh!

[Yue-Zhengyuan]

@VictorVanthilt Does the c4CTM implemented in TNRKit actually assumes a larger C4v symmetry?

https://github.com/VictorVanthilt/TNRKit.jl/blob/fde64f6738d0cc7b62158257a6a1bc7df913452a/src/schemes/ctm/c4ctm.jl#L89

This line looks a bit suspicious to me. If only C4 symmetry is assumed, naively I think there will be two projectors involved (instead of a single U)? Why do you "Hermitianize" the corner so only one projector is produced?

[dartsushi]

Sorry I assume C4v symmetry. More precisely 90 degrees rotation + complex conjugation (which does not matter in the real tensors)

[qiyang-ustc]

Just a quick note: in the new version, the efficiency of QRCTM is further improved, see https://github.com/qiyang-ustc/QRCTM/blob/dd160116c3d7b02076691ceaf0a9833511ae532d/heisenberg.py#L71
The only expensive operation is "T update" instead of "C update".